This invention relates to a device for cooling a web of material coming out of a drier, in particular a paper web of an offset printing machine coming out of a drier, which cooling device comprises a substantially closed housing with an inlet and an outlet slit for the web of material, said housing being provided at the outlet slit side with a feed aperture for feeding in outside air and at the inlet slit side with a discharge aperture for discharging air from the housing, the air being fed through the housing in counterflow to the direction of movement of the web of material.